Question

In one study of smokers who tried to quit smoking with nicotine patch​ therapy, 36 were smoking one year after treatment and 35 were not smoking one year after the treatment. Use a 0.10 significance level to test the claim that among smokers who try to quit with nicotine patch​ therapy, the majority are smoking one year after the treatment. Do these results suggest that the nicotine patch therapy is not​ effective?

What is the test statics and P value?

Answer 1

Given that, total number of smokers = 36 + 35 = 71

where, 36 were smoking one year after treatment.

=> sample proportion = 36/71 = 0.5070

The null and alternative hypotheses are,

H0 : p = 0.50

Ha : p > 0.50

This hypothesis test is a right-tailed test.

Test statistic is,

=> Test statistic = Z = 0.12

p-value = P(Z > 0.12) = 1 - P(Z < 0.12) = 1 - 0.5478 = 0.4522

=> p-value = 0.4522

Since, p-value is greater than 0.10 significance level, we fail to reject the null hypothesis (H0).

Conclusion : There not sufficient evidence to support the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment.